2nd Year Mathematics Notes

Practice82 MCQs & 63 exam questions with answers & mark schemes →

Every chapter of the mathematics syllabus for 2nd Year under the Punjab Board, in the order the book takes them. 10 lessons are published so far — each with notes, worked examples, a graph you can move, flashcards and a quiz — and more are being written.

Also called 12th Class, FSc Part 2, ICS Part 2, HSSC Part 2.

01

Graphical Representation of Functions

▸Functions and GraphsDomain, range, and the shapes you should recognise before plotting a point · 20 min · 8 questions→

02

Further Differentiation

▸CalculusRates of change, and areas under curves · 22 min · 6 questions→

03

Integration

▸IntegrationAdding up infinitely many infinitely thin slices · 22 min · 6 questions→

04

Differential Equations

▸Differential EquationsTurning a sentence about a rate of change into a function of time · 24 min · 8 questions→

05

Analytical Geometry

▸Introduction to Analytic GeometryLines as equations, and the standard distances worth memorising · 20 min · 8 questions→

06

Conic Sections

▸Conic SectionsFour curves, one cone, and the number that tells them apart · 22 min · 8 questions→

07

Kinematics

▸CalculusRates of change, and areas under curves · 22 min · 6 questions→

08

Numerical Methods

▸Numerical Solution of EquationsFinding a root when there is no formula to rearrange · 22 min · 8 questions→

09

Inverse Trigonometric Functions

▸Trigonometric Functions and their GraphsAmplitude, period and phase — three letters, three separate jobs · 20 min · 8 questions→

10

Solution of Trigonometric Equations

▸Trigonometric Identities and EquationsSix functions, a handful of identities, and how to pick the right one · 26 min · 8 questions→

11

Vector-Valued Functions

▸Vectors in SpaceThree dimensions, and the two ways of multiplying vectors · 22 min · 8 questions→

Frequently asked questions

What does 2nd Year Mathematics cover?

All 11 chapters — Graphical Representation of Functions, Further Differentiation, Integration, and more. The finished lessons carry notes, worked examples, an interactive diagram and a quiz; the remaining topics are mapped and being written.

Do these notes follow the Punjab Board syllabus?

Yes. They follow the 2nd Year Mathematics syllabus (2nd Year, 12th Class, FSc Part 2) under the Punjab Board, chapter by chapter, in the order the textbook takes them.

Are there practice questions or past-paper-style questions?

Yes — 82 multiple-choice questions and 63 exam-style questions with mark schemes, all with answers, on the 2nd Year Mathematics practice page.

Are the 2nd Year Mathematics notes free?

Yes — completely free, with no sign-up or login. Every topic has notes, worked examples, an interactive diagram you can change, flashcards and a quiz that explains each answer.